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Optimization and planning of radiation therapy is performed in a treatment planning system. This includes the definition of target structures to be irradiated and organs at risk to be protected, typically performed by contouring structures slice by slice in the image data. Conversions between contours and their volume representations are needed for visualizations and computations, but will however introduce a loss of information due to the sampling to a uniform voxel grid. The number of conversions performed can be large, causing errors to accumulate. The aim of this thesis is to examine volume reconstruction methods and sparse voxel representations for the purpose of volume reconstruction and representation with better accuracy than currently used algorithms in treatment planning systems. A prototype has been shown to be more accurate on contours and potentially cheaper in memory compared to the current method in RayStation in the case where contours represent non-smooth objects.

Distance field text rendering has many advantages compared to most other text renderingsolutions. Two of the advantages are the possibility  to scale the glyphs without losing the crisp edge and less memory consumption. A drawback with distance field text renderingcan be high distance field generation time. The solution for fast distance field text renderingin this thesis generates the distance fields by drawing distance gradients locally over the outlines of the glyphs. This method is much faster than the old exact methods for generating distance fields that often includes multiple passes over the whole image. Using the solution for text rendering proposed in this thesis results in good looking text that is generated on the fly. The distance fields are generated on a mobile device in less than 10 ms for most of the glyphs in good quality which is less than the time between two frames.

[pt] Sistemas CAD – Computer-Aided Design Systems – são muito utilizados nas diferentes etapas do ciclo de vida de um empreendimento de engenharia, como a elaboração do projeto conceitual, a construção da estrutura física e a operação da planta. A manutenção das instalações é uma tarefa de muita importância durante a operação, onde a pintura de equipamentos e estruturas é essencial. Estimar a área de pintura dos diferentes objetos possui um custo elevado se feito manualmente, com a utilização de trenas e lasers. Uma forma mais eficiente de calcular essas áreas é através do uso das ferramentas CAD. Entretanto, o processo de modelagem do modelo CAD, utilizando objetos paramétricos e malhas tridimensionais, insere superfícies que estão encobertas por outros objetos. Essas superfícies encobertas não são pintadas, e considerar suas áreas na orçamentação da pintura resulta em erros consideráveis. Portanto, o uso de um cálculo simples de todas as áreas de superfícies que compõem os objetos não é adequado. Com o objetivo de eliminar as superfícies escondidas do cálculo da área de pintura, este trabalho propõe uma abordagem baseada em campos de distância adaptativos juntamente com operações de geometria sólida construtiva. Primeiramente, as malhas passam por uma fase de pré-processamento, no qual são ajustadas de forma que cumpram com os requisitos necessários para a construção do campo de distância adaptativo, e em seguida os seus campos são calculados. Objetos parametrizados não necessitam dessa etapa pois já possuem um campo de distância implícito. Operações de geometria sólida construtiva foram então utilizadas para obter o campo da diferença e da interseção de cada objeto com a cena. De posse desses dados, foi desenvolvida uma fórmula que utiliza as áreas da diferença com a cena, da interseção e a área superficial de cada objeto para calcular a sua área de pintura. Em testes controlados, as áreas de pintura obtidas diferenciaram em no máximo 0,84 por cento das áreas reais. Nos testes com modelos reais, foi obtido uma redução de até 38 por cento da área estimada em relação a abordagem simplista de não tratar as superfícies ocultas. / [en] CAD Systems – Computer-Aided Design Systems – are widely used in the different life cycle stages of an engineering enterprise, such as conceptual design, physical structure construction, and plant operation. The maintenance of the facility is a very important task during the operation, where painting the equipments and structures is essential. Estimating the painting area of the different objects has a high cost if done manually, using measuring tapes and lasers. A more efficiently way to calculate these areas is through the use of CAD tools. However, the modeling process of the CAD model, using parametric objects and three-dimensional meshes, inserts surfaces that are hidden by other objects. These hidden surfaces are not painted, and considering their areas in the painting budgeting leads to considerable errors. Therefore, the use of a simple calculation of all the surfaces areas that compose the objects is not adequate. With the objective of eliminating the hidden surfaces of the painting area computation, this work proposes an approach based on adaptive distance fields together with constructive solid geometry operations. Firstly, the meshes pass through a preprocessing phase, in which they are adjusted to fulfill the requirements for the adaptive distance field construction, and then their fields are computed. Parametrized objects do not need this step because they already have an implicit distance field. Constructive solid geometry operations were then used to obtain the difference and the intersection fields of each object with the scene. With this data, the painting areas are calculated considering the areas of the difference with the scene, the intersection and the surface area of each object. In controlled tests, the painting areas obtained differs of a maximum of 0.84 percent of the real areas. In tests with real models, a reduction of up to 38 percent of the estimated area was obtained in relation to the simplistic approach of not treating hidden surfaces.

This thesis extends the utility of the Monte Carlo approach to PDE-based methods presented in the paper Monte Carlo Geometry Processing. In particular, we implement this method on the GPU using CUDA, and investigate more viable methods of estimating the source integral when solving Poisson’s equation with intricate source terms. This is the case for a large group of gradient-domain methods in computer graphics, where source terms are represented by discrete volumetric data on regular grids. We develop unbiased source integral estimators like image-based importance sampling (IBIS) and biased estimators like source integral caching (SIC) and evaluate these against existing GPU-accelerated finite difference solvers for gradient-domain applications. By decoupling the source integration step from the WoS-algorithm, we find that the SIC method can improve performance by several orders of magnitude, making it competitive with existing finite difference solvers in many cases. We further investigate the viability of distance fields for accelerated distance queries and find that these can provide significant performance improvements compared to BVHs without meaningfully affecting bias. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>